Publication number | US5549387 A |

Publication type | Grant |

Application number | US 08/252,597 |

Publication date | Aug 27, 1996 |

Filing date | Jun 1, 1994 |

Priority date | Jun 1, 1994 |

Fee status | Paid |

Also published as | DE69532851D1, DE69532851T2, EP0763196A1, EP0763196A4, EP0763196B1, US6170984, WO1995033200A1 |

Publication number | 08252597, 252597, US 5549387 A, US 5549387A, US-A-5549387, US5549387 A, US5549387A |

Inventors | Jurgen Schawe, Marcel Margulies |

Original Assignee | The Perkin-Elmer Corporation |

Export Citation | BiBTeX, EndNote, RefMan |

Patent Citations (65), Non-Patent Citations (105), Referenced by (16), Classifications (13), Legal Events (7) | |

External Links: USPTO, USPTO Assignment, Espacenet | |

US 5549387 A

Abstract

The invention is directed to a differential analysis method and apparatus wherein a sample and reference are subjected to an externally applied disturbance, such as temperature change, in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part, and the measured differential signal is processed into real and imaginary components relating, respectively, to the energy storage and energy loss portions of the signal.

Claims(18)

1. A differential analysis apparatus comprising:

means for holding a sample and means for holding a reference;

means for subjecting the sample in the sample means and a reference in the reference means to an externally applied disturbance in acccord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part;

means for receiving data representative of differential signals resulting from the sample and the reference being subjected to the externally applied disturbance in accord with the prescribed function; and

means for processing the data to provide at least one characteristic parameter of the sample and to separate the at least one parameter directly into components relating to an energy storage portion and an energy loss portion of the at least one parameter.

2. The apparatus of claim 1 wherein the apparatus is a power compensation differential scanning calorimetry instrument.

3. The apparatus of claim 1 wherein the apparatus is a heat flux differential scanning calorimetry instrument.

4. The apparatus of claim 1 wherein the periodically changing part comprises a sinusoidal function and the linearly changing part comprises a linear cooling or heating scan, wherein the sinusoidal function is superimposed on the linear cooling or heating scan.

5. The apparatus of claim 1 wherein the characteristic parameter is heat capacity.

6. A method of analyzing a sample using a differential analysis apparatus comprising:

subjecting the sample and a reference to an applied disturbance in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part;

detecting a differential signal representative of at least one characteristic parameter of the sample; and

processing the signal directly into components relating to an energy storage portion and an energy loss portion of the at least one parameter.

7. The method of claim 6 wherein the applied disturbance is temperature change.

8. The method of claim 7 wherein the characteristic parameter is heat capacity.

9. A method of analyzing a sample using a differential analysis apparatus comprising:

subjecting the sample and a reference to an externally applied disturbance in accord with a prescribed function comprising a periodically changing part having a specified frequency;

detecting a differential signal representative of at least one characteristic parameter of the sample;

processing the signal to determine a factor relating to a universal calibration function, wherein said processing utilizes data collected during the analysis of the sample and does not require collecting data during a separate calibration experiment; and

using the factor relating to the universal calibration function to provide an energy loss portion and an energy storage portion of the characteristic parameter.

10. The method of claim 9 wherein the applied disturbance is temperature change.

11. The method of claim 10 wherein the characteristic parameter is heat capacity.

12. The method of claim 10 wherein the periodically changing part comprises a sinusoidal function, and wherein the prescribed function further comprises a linearly changing part comprising a linear cooling or heating scan, wherein the sinusoidal function is superimposed on the linear cooling or heating scan.

13. The method of claim 10 wherein the characteristic parameter relates to a time-dependent thermal event of the sample.

14. A differential analysis apparatus comprising:

a sample holder and a reference holder;

a thermal device for subjecting a sample in the sample holder and a reference in the reference holder to a temperature change in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part;

computing means for (i) receiving data representative of differential signals resulting from the sample and the reference being subjected to the temperature change in accord with the prescribed function, and for (ii) processing the data to provide at least one characteristic parameter of the sample and to separate the at least one parameter directly into components relating to an energy storage portion and an energy loss portion of the at least one parameter.

15. A method of analyzing a sample using a power compensated differential scanning calorimeter comprising:

subjecting the sample and a reference to a temperature change in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part having a specified frequency and a specified amplitude;

detecting an amplitude signal and a phase signal, measured with respect to a phase of the prescribed function, of a differential power signal; and

processing the amplitude signal and the phase signal directly into components relating to an energy storage portion and an energy loss portion of a complex specific heat derived from the differential power signal.

16. A method of analyzing a sample using a power compensated differential scanning calorimeter comprising:

subjecting the sample and a reference to a temperature change in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part having a specified frequency and a specified amplitude;

detecting an amplitude signal and a phase signal, measured with respect to a phase of the prescribed function, of a differential power signal;

processing the amplitude signal and the phase signal to determine a factor relating to a universal calibration function; and

using the factor relating to the universal calibration function to provide separate components relating to an energy storage portion and an energy loss portion of a complex specific heat derived from the differential power signal.

17. A method of analyzing a sample using a heat flux differential scanning calorimeter comprising:

subjecting the sample and a reference to a temperature change in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part having a specified frequency and a specified amplitude;

detecting an amplitude signal and a phase signal, measured with respect to a phase of the prescribed function, of a differential heat flow signal; and

processing the amplitude signal and the phase signal directly into components relating to an energy storage portion and an energy loss portion of a complex specific heat derived from the differential heat flow signal.

18. A method of analyzing a sample using a heat flux differential scanning calorimeter comprising:subjecting the sample and a reference to a temperature change in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part having a specified frequency and a specified amplitude;

detecting an amplitude signal and a phase signal, measured with respect to a phase of the prescribed function, of a differential heat flow signal;

processing the amplitude signal and the phase signal to determine a factor relating to a universal calibration function; and

using the factor relating to the universal calibration function to provide separate components relating to an energy storage portion and an energy loss portion of a complex specific heat derived from the differential heat flow signal.

Description

The present invention relates to a method and apparatus for differential thermal analysis. Differential thermal techniques generally consist of applying heat simultaneously to a sample material and a reference material and measuring a parameter, such as differential power input, as the sample goes through a physical or chemical change. In differential thermal analysis (DTA), the sample and reference are heated or cooled according to a programmed rate, and the temperature differential between the sample and reference is measured as the scan proceeds. In differential scanning calorimetry (DSC), differential power rather than differential temperature is measured. The differential power represents the difference in energy required to maintain the sample and reference in accord with a heating or cooling program.

In addition to DSC and DTA, other differential thermal techniques also exist to measure basic properties that change with temperature. In differential dielectric analysis (DDA) a property of the sample (dielectric constant) is measured while the temperature is changed. Further, in differential thermogravimetric analysis (DTGA), differential weight loss of a sample is monitored as the temperature is increased.

In 1968, Sullivan and Seidel reported a non-differential thermal technique which is now known as AC calorimetry. P. F. Sullivan, G. Seidel, "Steady-State, AC-Temperature Calorimetry, " Phys. Rev. 173(3), 679-685 (1968). This technique was later modified by Dixon et al. who, in 1982, reported a method called differential AC calorimetry. G. S. Dixon et al., "A Differential AC Calorimeter for Biophysical Studies," Anal. Biochem. 121(1), 55-61 (1982). Differential AC calorimetry, as described by Dixon et al., consists of heating or cooling the sample and reference at a linear rate with a sinusoidal oscillation superimposed on the linear heating or cooling program. Dixon et al. determined the heat capacity of the sample using the differential AC temperature response measured between the sample and reference.

U.S. Pat. No. 5,224,775, assigned to TA Instruments, Inc. (hereinafter "the '775 patent"), discloses the use of differential AC calorimetry in a method which deconvolutes the resulting differential signal as described by Dixon et al. The '775 patent discloses processing of the signal into "rapidly reversing" and "non-rapidly reversing" components. The thermodynamic significance of the "rapidly reversing" and "non-rapidly reversing" components is not apparent for time-dependent processes. For time-independent thermal events (equilibrium processes), only the "rapidly reversing" component may have thermodynamic significance. Since most thermal events of interest, such as the glass transition of a polymeric material, are time-dependent processes, there is an obvious need for a more comprehensive method of processing the differential signal.

The present invention provides a method and apparatus for processing the differential signal into real (inphase) and imaginary (quadrature) components which are related to the "energy storage" and "energy loss" portions of the thermal event being studied. The inphase and quadrature components provide physical and thermodynamic information for thermal events which are time-independent or time-dependent.

FIG. 1 is a schematic diagram illustrating a "power compensation" differential scanning calorimeter, which includes two control loops and is adapted to implement the present invention.

FIG. 2 is a schematic diagram illustrating a DTA instrument which is adapted to implement the present invention.

FIG. 3 is a schematic diagram illustrating a "heat flux" differential scanning calorimeter which is adapted to implement the present invention.

FIG. 4 is a plot of heat capacity vs. temperature with data representing average heat capacity, the energy storage (real) portion of the heat capacity and the energy loss (imaginary) portion of the heat capacity which are obtained according to the method and apparatus of the present invention.

FIG. 5 is a plot of heat capacity vs. temperature with data representing average heat capacity, the absolute value of the heat capacity and the difference between the average and absolute heat capacity.

FIG. 6 is a plot of heat capacity vs. temperature with data representing the energy loss (imaginary) and energy storage (real) portions of the heat capacity, the absolute value of the heat capacity and the difference between the average and absolute heat capacity which are obtained according to the method and apparatus of the present invention.

FIG. 7 is a plot of heat capacity vs. temperature with data representing the energy loss (imaginary) and energy storage (real) portions of the heat capacity, and the average heat capacity which are obtained according to the method and apparatus of the present invention.

FIG. 8 is a plot of heat capacity vs. temperature with data representing the energy loss (imaginary) and energy storage (real) portions of the heat capacity, the absolute and average values of the heat capacity and the difference between the average and absolute heat capacity.

FIG. 9 is a plot of heat capacity vs. temperature with data representing the energy loss (imaginary) and energy storage (real) portions of the heat capacity, and the average heat capacity which are obtained according to the method and apparatus of the present invention.

FIG. 10 is a plot of heat capacity vs. temperature with data representing the absolute and average values of the heat capacity and the difference between the average and absolute heat capacity.

FIG. 11 is a plot of heat capacity vs. temperature with data representing the energy loss (imaginary) and energy storage (real) portions of the heat capacity, the absolute and average values of the heat capacity and the difference between the average and absolute heat capacity.

FIG. 12 is a graph representing an interpolation method for determining φ_{g}.

The invention is directed to a differential analysis apparatus comprising (i) a sample holder and a reference holder, (ii) a thermal device for subjecting the sample and reference to an externally applied disturbance, such as temperature change, in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part (iii) at least one computing device for receiving data representative of differential signals resulting from the sample and reference being subjected to the applied disturbance in accord with the prescribed function, and (iv) a device to process said data to provide at least one parameter, such as heat capacity, representative of said sample and to separate said at least one parameter into components relating to the energy storage (real) and energy loss (imaginary) portions of said at least one parameter.

The invention further comprises a method of analyzing a sample using a differential analysis apparatus comprising (i) subjecting a sample and reference to an externally applied disturbance, such as temperature change, in accord with a prescribed function comprising the sum of a linearly changing part and a periodically changing part, (ii) detecting a differential signal representative of at least one characteristic parameter of the sample, and (iii) processing said signal into components relating to the energy storage and energy loss portions of said at least one characteristic parameter.

The present invention finds application in differential analysis methods and apparatus including, but not limited to, DTA, DSC, DDA, and differential photocalorimetry (DPC). While the following detailed description is provided with reference to DSC and DTA, the present invention is not limited to an apparatus comprising, or method employing, DSC and DTA. Further, a sinusoidal periodic function is adopted for the following description. However, the invention is not so limited, and any periodic function can be substituted for the sinusoidal function. The term "prescribed function" as used herein means any function which comprises the sum of a linearly changing part and a periodically changing part. The periodically changing part includes, but is not limited to, a sinusoidal function, a saw tooth function, a square wave function, or a pulse wave. While all periodic functions can be characterized by a period or frequency, certain periodic functions, such as sinusoidal functions, are also characterized, in addition, by an amplitude.

The linearly changing part can have a positive (heating), negative (cooling), or zero slope. In the case where the slope is zero, the prescribed function includes "isothermal functions" in which the sample and reference are subjected to a periodic temperature variation such that during the scan the average temperature of the sample and reference remains essentially constant.

FIG. 1 illustrates a portion 10 of a DSC, for example, a Perkin-Elmer Corporation DSC-7 type of calorimeter, which can be used to implement the present invention. The user's manual to the DSC-7 calorimeter, entitled "Users Manual, 7 Series/Unix DSC7, Differential Scanning Calorimeter," is herein incorporated by reference. This instrument measures the differential power required to keep both sample and reference sensors 44, 54 at the same temperature throughout the DSC experiment. The apparatus, as illustrated, is described and explained in basic terms in E. S. Watson et al., "A Differential Scanning Calorimeter for Quantitative Differential Analysis, " Anal Chem. 36(7), 1233-1238 (1964), which is herein incorporated by reference.

In FIG. 1, reference and sample containers 56 and 58, respectively, are mounted on platforms 52 and 46. The reference generally is a standard (or simply the empty container) and the sample is a material having some characteristic parameter to be compared with that of the standard. As used herein, the term "characteristic parameter" means any property representative of the sample which is measured differentially with respect to the reference. Characteristic parameters include, but are not limited to, differential power input, differential heat flow, differential temperature, dielectric constant, and differential weight loss.

The reference 56 and sample 58 are subjected to a programmed heating or cooling program, in accord with a prescribed function, through a process of programmed and balanced heating. The programmed heating or cooling run subjects the sample and reference to an externally applied disturbance. The term "applied disturbance", as used herein, means a physical stress applied to both the sample and reference which permits, in accord with the differential technique used, the measurement of a characteristic parameter of the sample. In DSC and DTA, the applied disturbance is heat which induces a change in temperature (though not a change in average temperature if an isothermal function is used). In DDA, the applied disturbance is an electrical field. In DPC, the applied disturbance is a lightwave.

Both the programmed heating and the balanced heating are performed through the reference heater 50 and the sample heater 48 in the reference and sample bases 52, 46. The heaters are powered with alternating current, and on one half-cycle the power supplied to both heaters is controlled by the temperature programmer 60. On the other half-cycle, however, a different power is supplied to each heater to nullify any temperature differential between the sample and the reference as sensed with the platinum resistance thermometers 54, 44 in the container bases. Thus, the heating system has two control loops, one responding to the temperature program and the other responding to the different energy requirements of the sample and reference. The average temperature amplifier 62, average temperature computer 64, recorder 68 and differential temperature amplifier 66 interact to maintain the two control loops as explained with respect to FIG. 1 in the following paragraph. The instrument responds very rapidly so that the deviation of the sample temperature from the reference temperature is negligible, and therefore the sample temperature follows the predetermined program even though it may undergo a thermal event (such as a phase or glass transition).

The system of FIG. 1 can be divided into two separate control loops, one loop for average temperature control and the other for differential temperature control. In the average temperature control loop, the programmer 60 provides a signal which is proportional to the desired temperature of the sample holder 58 and the reference holder 56. The programmer information is also relayed to the recorder 68 and appears as the abscissa scale marking. The programmer signal reaches the average temperature amplifier 62 and is compared with signals received from resistance thermometers 54, 44 via the average temperature computer 64. If the average temperature is greater than the temperature called for by the programmer 60, then the power supplied to the sample and reference heaters 48, 50 is decreased, and vice versa if the average temperature is less than that called for by the programmer 60.

In the differential temperature control loop, temperature signals received from the resistance thermometers 44, 54 are relayed to the differential temperature amplifier 66 via a comparator circuit (not shown) which determines whether the sample or reference temperature signal is greater. The differential temperature amplifier 66 responds to a disparity in the sample and reference temperature signals by adjusting the differential power increment fed to the sample and reference heaters 48, 50 to correct the temperature difference. A signal proportional to the differential power is sent to the recorder 68. The recorder 68 relays the differential signal to computing device 69 which processes the signal to provide the user with the characteristic parameter of the sample. Such computing devices include any appropriate commercially-available device, including desktop personal computers, such as the Perkin-Elmer Unix 7-Series data station.

The foregoing description relating to FIG. 1 is directed to "power compensation" DSC. The structure of the apparatus for the present invention also includes instrumentation for "heat flux" DSC, as depicted in FIG. 3, and differential thermal analysis (DTA), as depicted in FIG. 2. Unlike "power compensation" DSC, the signal obtained in DTA or "heat flux" DSC is derived from the temperature difference between the sample and reference. The distinction between DTA and heat flux DSC is not substantial, and thus it is possible to calibrate a differential thermal analyzer for use as a heat flux DSC. Such a modification is described in F. Hongtu, P. G. Laye, Thermochim. Acta 153, 311 (1989).

In power compensation DSC, the sample and reference are provided with individual heaters. As shown in FIG. 2, the DTA technique provides an instrument 96 with a single heater 72 for both sample 70 and reference 74. Heat flux DSC, as shown in FIG. 3, provides an instrument 94 with a single heater 82 which heats both sample 88 and reference 90. In DTA, the temperatures of the sample and reference are detected, respectively, by sensors 76 and 80 which can be imbedded in the sample and reference materials. Heat flux DSC, on the other hand, uses a sample temperature sensor 86 and a reference temperature sensor 84, which are attached to a conductive membrane under pans which hold the sample and reference materials. In both DTA and heat flux DSC, the differential temperature 80 (FIG. 2) and 92 (FIG. 3) is determined. The DTA and heat flux DSC techniques, while considered to be inherently less quantitative than DSC, can be used to implement the method and apparatus of the present invention.

Employing a conventional DSC, the sample and reference are heated or cooled at a constant rate β_{o}. The measurement signal represents the differential heat flow required to maintain the rate β_{o}.

In one embodiment of the present invention, a sinusoidal temperature oscillation is superimposed on the linear temperature change β_{o}, so that the temperature of sensing elements 44, 54 (FIG. 1) obeys eq. (1):

T(t)=T_{0}+β_{0}t+T_{a}sin ω_{0}t (1)

where T_{o} is the initial temperature, T_{a} is the amplitude of the sinusoidal temperature change, and ω_{o} is the cyclic frequency.

The method disclosed in the '775 patent proceeds from the assumption that the following is valid for the measured heat flow Φ (see for example sq. (1) in M. Reading et al., "Some Aspects of the Theory and Practice of Modulated Differential Scanning Calorimetry", Proceedings of the 1992 NATAS Conference, at page 145): ##EQU1## where C_{p} is the heat capacity of the sample, and f(t,T) describes the kinetic component of the DSC signal due to any physical or chemical transformation.

Interpreting eq. (2), if the heat capacity is determined by an independent method, then, according to the prior art, from a conventional DSC curve the kinetic component can be obtained using simple subtraction.

Phenomenologically, one can describe the measured heat flow as follows:

φ(T)=Φ_{D}(T)+Φ_{a}(T) cos (ω_{0}t+ψ)(3)

where Φ_{D} is identical to the conventional DSC signal.

From the amplitude of the modulated component Φ_{a} the heat capacity is calculated thus: ##EQU2##

One then obtains the "rapidly reversible" component (Φ_{rev}) of the measured signal as follows:

Φ_{rev}(T)=C_{p}(T)·β_{0}(5)

The kinetic component ("non-rapidly reversible" heat transfer) is then

Φ_{non}(T)=Φ_{D}(T)-Φ_{rev}(T) (6)

These equations follow the method disclosed in the '775 patent.

If a physical system is in equilibrium, then no energy loss (dissipation) occurs, and the entropy remains unchanged (second law of thermodynamics). The system can then be described by time-independent potentials and the material properties are described by time-independent parameters (such as dielectric constant, compressibility modulus or heat capacity). In this case the DSC measurement curves are described, excluding the effects of thermal conduction, by equilibrium thermodynamics.

However, many thermal events are dependent on time and linked with energy loss (dissipation, or entropy change). Such events include biological processes, chemical reactions, glass transitions, and kinetically determined phase transitions. If the system is near equilibrium and if disturbances of the system during measurement are sufficiently small-scale, these events can be described by a linear response theory (see R. Kubo, Rep. Prog. Phys. 29, 255(1966)).

If the measurement involves a disturbance by an intensive variable (such as temperature), then an extensive variable is measured (such as enthalpy H). In accord with the present invention, the relevant material property of the sample (such as heat capacity) can then be associated with an auto-correlation or retardation function φ(t).

Most generally, one can write a relationship between variations in temperature and the corresponding variations in enthalpy as follows: ##EQU3## Eq. (7) provides an implicit definition of the auto-correlation function. One may then define a frequency-dependent complex heat capacity in the following manner: ##EQU4## with

C(ω)=C'(ω)+C"(ω) (9)

where i is the imaginary unit (i=√-1)

The real portion of the heat capacity C' describes energy storage, and in an equilibrium case matches C_{p}. As used herein, the terms "real" component (or portion) and "energy storage" component are interchangeable. The imaginary portion C" relates to the energy loss, and thus the terms "imaginary" component (or portion) and "energy loss" component are interchangeable.

In DSC measurements, heat flow ##EQU5## is the measurement variable.

By inserting eq. (10) into eq. (7), one obtains the following for the measurement signal: ##EQU6##

For the case of linear systems, eq. (11) is the correct tool for describing a differential thermal instrument employing a prescribed function comprising a periodic part superimposed on a linear scan. This equation stands in contrast to eq. (2) of the prior art.

Isothermal conditions, as described here, mean that the temperature is altered according to a periodic function (a sinusoidal function in the following eqs.) with a sufficiently small amplitude T_{a} about a constant temperature T_{o} :

T(t)=T_{0}+T_{a}sin (ω_{0}t) (13)

For the temperature change β, it follows that

β(t)=ω_{0}T_{a}cos (ω_{0}t) (14)

Insertion of equation eq. (14) into eq. (11) yields ##EQU7## with the solution:

Φ(t)=ω_{0}T_{a}[C'(ω_{0}) cos (ω_{0}t)+C"(ω_{0}) sin (ω_{0}t)] (16)

or

Φ(t)=ω_{o}T_{a}|C(ω_{o})| cos (ω_{o}t-ψ) (17)

with ##EQU8##

The solution represented by eq. (16) is the result of the following derivation (eqs. (A2)-(A5)). The Fourier transformation of a convolution product (eq. 15) reduces to a simple algebraic product according to:

ℑ(Φ(t))=Φ(ω)=1/2ω_{0}T_{a}φ(ω)[δ(ω-ω_{0})+δ(ω+ω.sub.0)] (A2)

where δ(ω) is the Dirac function.

The inverse transformation of eq. (A2) then yields the time-dependent heat flow: ##EQU9##

Since φ(ω)=C*(ω)=C*(ω) (see eq. (8)) and since φ(ω)=φ*(-ω) because φ(t) is real, it follows that:

Φ(t)=ω_{0}T_{a}Re[C(ω_{0})e^{i}ω.sbsp.0^{t}] (A4)

or

Φ(t)=ω_{0}T_{a}[C'(ω_{0}) cos (ω_{0}t)+c"(ω_{0}) sin (ω_{0}t)] (A5)

If Φ_{a} is the heat flow amplitude (see eq. (17)), then one obtains the amplitude of the complex heat capacity from ##EQU10##

From this quantity, and the phase shift between heat flow and temperature, ψ, the energy storage and energy loss components of heat capacity can be determined. In general the two components are functions of the measurement frequency.

A comparison of sq. (20) and eq. (4) shows that the two equations are identical only when C"(ω_{o})=0 is valid. However, this is only realized if the heat capacity is not time-dependent (equilibrium). A correct interpretation of time-dependent processes in non-equilibrium thus appears not to be possible with prior art methods.

If a sinusoidal oscillation function is superimposed on a linear heating rate β_{o}, the following can be written:

T(t)=T_{0}+β_{0}t+T_{a}sin (ω_{0}t) (21)

β(t)=β_{0}+ω_{0}T_{a}cos (ω_{0}t)(22)

As eq. (3) shows, the measured heat transfer is composed of the superposition of a non-periodic function on a periodic one. So that the phase shift φ and the amplitude Φ_{a} may be determined with sufficiently small error, it is necessary that the non-periodic component be regarded as constant at least for one period of the periodic component. For this, it is required to have a thermal event that evolves sufficiently slowly and a low heating rate.

β_{o} may be considered sufficiently small if: ##EQU11##

Under this condition, one obtains through insertion of eq. (22) into (11):

Φ(T)=C.sub.β (T)β_{0}+ω_{0}T_{a}|C(T,ω_{0})| cos (ω_{0}t-ψ)(24)

C.sub.β does not correspond to the equilibrium heat capacity C_{p}, but rather to that which is determined from a conventional DSC measurement with a linear heating rate of β_{o}.

If a pure relaxation transition is investigated, one obtains the overall information (the complex heat capacity) directly from the periodic component of the heat flow.

In order to compare the prior art method with the present invention, we consider the simplest model to describe the time dependence of a dynamic system, in which the retardation function corresponds to an exponential function, and neglect the effect of non-equilibrium. Then the following is valid for the complex heat capacity: ##EQU12## where C_{p} is the heat capacity in equilibrium (ω→0), C.sub.∞ the heat capacity for ω→∞, and τ the relaxation time.

With a sinusoidal function superimposed on a linear heating scan, C_{p} is replaced by C.sub.β. From the amplitude of the periodic component one determines the amplitude of the complex heat capacity (see eq. (20)). To obtain the "non-rapidly reversible" heat flow Φ_{non}, in accord with the prior art method, |C| is subtracted from C.sub.β (see eqs. (6) and (24)). By insertion of eq. (25) into eq. (24), it is possible to verify that the following is valid: ##EQU13## For the "rapidly reversible" heat flow one obtains: ##EQU14##

The derivation of eqs. (28) and (29) follows from eqs. (A6)-(A10) as described below. By elimination of ωτ from eqs. (26) and (27) one obtains the equation (Cole-Cole-Bergen): ##EQU15## Following elementary transformations one obtains:

|C|^{2}=C'^{2}+C"^{2}=C'(C_{p}+C.sub.∞)-C_{p}C.sub.∞ (A 7)

Assuming that:

C_{p}C.sub.∞ ≈C'C_{p}(A 8)

it follows that:

|C|^{2}=C'C_{p}(A 9)

from which eq. (29) follows for the "rapidly reversible" heat flow.

For the "non-rapidly reversible" heat flow, ##EQU16## from which eq. (28) follows.

Only C.sub.β and C' contribute to the development of a peak in Φ_{non}. With the prior art method there can never be a separation of the energy loss processes since C"(ω_{o}) is not contained in eq. (28). Φ_{non} is merely the difference between two measurements obtained under dissimilar experimental conditions and is not amenable to physical interpretation.

From eqs. (20), (28) and (29) it is evident that the prior art method provides results that can be correctly interpreted only under equilibrium conditions. Since, in such a case, C'=C_{p} and C"=0, it follows that

Φ_{rev}=C_{p}β_{o}(30)

and

Φ_{non}=0 (31)

In assessing glass transitions, more significant information is gained if determinations are made of the energy storage component of heat flow:

Φ_{stor}(T,ω_{0})=C'(T,ω_{0})β_{0}=|C(T,ω_{0})|β_{0}cos ω(32)

and the energy loss component of heat flow

Φ_{loss}(T,ω_{0})=C"(T,ω_{0})β_{0}=C(T,ω_{0})|β_{0}sin ω (33)

Only the energy storage and energy loss components of the heat flow have thermodynamic and physical significance for both time-dependent and time-independent thermal events.

If a time-dependent reaction occurs, then on neglecting the entropy variation, we find: ##EQU17## where mq_{p},T is the heat of reaction

ν is the rate of reaction

f_{T} (t) is the heat flow measured under isothermal conditions.

To find the heat flow during a temperature scan, it is necessary to know the temperature dependence of f (α_{f} =df/dT). Using a linear approximation and the principle of superposition, we find for the relevant part of the heat flux: ##EQU18##

If the measurement is started at a sufficiently low temperature, the first term on the right hand side of eq. (35) may be neglected. A comparison of eqs. (11) and (35) indicates that the principle underlying data reduction in the present case will be identical to that explained previously. However, the interpretation of the results will be different.

If the sample is sufficiently far removed from its actual equilibrium state, then the linear approximation is no longer valid. In this case, Φ_{r} contains no information on such reactions, which, therefore, can be detected only in the conventional DSC signal (or the averaged heat flow Φ_{D}). C'(T)β_{o} may then be used as a baseline for the analysis of the DSC signal measured in such reactions.

The temperature sensor of a DSC is not directly in contact with the sample. Between the sample and the sensor, and within the sample itself, there is some thermal resistance to heat flow. Therefore, there is a difference between the measured temperature T and the sample temperature T_{s}. For the case of an isothermal, sinusoidally oscillated scan, the following is valid for the sample temperature:

T_{s}(t)=T_{0}+T_{a}sin ω_{0}t (36)

The corresponding temperature change is

β_{s}(t)=ω_{0}T_{a}cos ω_{0}t (37)

The effect of the thermal resistance on the measurement signal may be assessed as follows: ##EQU19##

G(t) is the function through which the thermal resistance is described. G(t) is real.

By solving equation (39) and inserting its solution into equation (11), one obtains the following for the measured heat flow:

Φ(t)=ω_{0}T_{a}|G(T,ω_{0})||C(T,ω_{0}).vertline. cos (ω_{0}t-ω-ω_{g}) (40)

The solution follows from eqs. (A11)-(A17).

Insertion of eq. (37) into eq. (39) and the subsequent Fourier transformation of the convolution product yields, similarly to eq. (A2):

β(ω)=1/2ω_{0}T_{a}G(ω)[δ(ω-ω_{0})+δ(ω+ω_{0})](A11)

By Fourier transformation of eq. (11),

Φ(ω)=φ(ω)β(ω) (A12)

Using eq. (A11),

Φ(ω)=1/2ω_{0}T_{a}C*(ω)G(ω)[δ(ω-ω_{0})+δ(ω+.omega._{0})] (A13)

The inverse transformation yields

Φ(t)=1/2ω_{0}T_{a}[C*(ω_{0})e^{i}ω.sbsp.0^{t}+C*(-ω_{0})G(-ω_{0})e^{-i}ω.sbsp.0^{t}](A14)

Since G(t) is real, G(ω)=G*(-ω). Hence,

Φ(t)=ω_{0}T_{a}Re[C*(ω_{0})e^{i}ω.sbsp.0^{t}] (A15)

or ##EQU20##

It can be recognized that the amplitude of the heat flow is modified by |G|, and that owing to the thermal resistance, an additional phase shift ψ_{g} comes into existence.

This influence of thermal conduction can be eliminated by means of a calibration. For this, a substance is needed with no energy loss component in its heat capacity, such as sapphire.

The calibration factor for the amplitude is obtained from ##EQU21## When using the sapphire standard, the phase shift between temperature and heat flow is ψ_{g}.

It can be shown that the calibration factor K is of the form

K=K(ω_{0},T_{a},T) (42)

where k, is the heat transfer coefficient between the sample and the temperature sensor. In the case of sufficiently thin samples, it can be shown that the above function (42), in fact, reduces to K'(ω_{0}, ψ) where ψ is the heat flow phase, measured in the absence of any time-dependent thermal event. The calibration factor K, or K'(ω_{0}, ψ), represents a universal calibration function which incorporates implicitly physical properties of the sample (e.g., heat transfer) through its dependence on ψ. This function can be determined for any instrument (whether a DTA or a DSC of the heat flux or power compensation type) using a known standard, such as sapphire. Once obtained it can be used in a wide range of temperatures, scanning rates or oscillation periods and allows the user to measure absolute (as opposed to relative) values of the complex specific heat for any sample.

The following is a step-by-step description of an embodiment of the method and apparatus of the invention. Other embodiments will be apparent to those skilled in the art.

The user selects a linear temperature program that consists of any number of heating or cooling scans, each of which is preceded and followed by an isothermal segment. The user also selects an oscillation period and an oscillation amplitude.

The instrument 10 (FIG. 1) records the sample temperature, as measured by the sensor 44 located close to the sample material, and, for a power compensation DSC, the differential power that is applied to maintain the sample and the reference at the same temperature throughout the applied temperature program. For a heat flux DSC, the instrument 94 (FIG. 3) records the sample temperature as measured by a sensor 86 located close to the sample material and the differential heat flow. In a DTA instrument 96 (FIG. 2), a sensor 76 imbedded in the sample material measures the sample temperature and the differential heat flow. The recorded signals are analyzed over a moving interval in order to retrieve the analytically significant information.

The analysis proceeds in accord with the following steps:

1. Extract the conventional DSC signal and temperature: At each point, the normalized numerical integral of the heat flow and temperature, over an interval consisting of exactly an integer number of oscillation periods and centered on that point, is calculated. The results represent the average heat flow and average temperature associated with the centroid of the integration interval. These quantities will be referred to as the DC signals (φ_{DC} and T_{DC}).

2. Extract the pure oscillated heat flow and temperature signals: On a point by point basis, the DC signals (φ_{DC} and T_{DC}) are subtracted from the recorded signals. This operation yields the pure oscillated signals, which will be referred to henceforth as the AC signals (φ_{AC} and T_{AC}).

3. Calculate the in-phase and in-quadrature components of the AC signals: At each point, the numerical integral of the AC signals (φ_{AC} and T_{AC}) suitably multiplied by sine and cosine functions, over an interval consisting of exactly an integer number of oscillation periods and centered on that point, is calculated. Using the orthogonality property of circular functions over an integer number of periods, the inphase (φ_{sin} and T_{sin}) and quadrature (φ_{cos} and T_{cos}) components of the AC signals can be derived from the integration results. Each component is associated with the centroid of the integration interval.

4. Calculate the actual heat flow phase ψ_{g} : At each point of an underlying isotherm, the difference between the measured heat flow phase (ψ_{m} =tan^{-1} (φ_{sin} /φ_{cos})) and the temperature phase (ψ_{T} =-tan^{-1} (φ_{cos} /φ_{sin})) is obtained (ψ_{g} =ψ_{m} -ψ_{T}. The value of ψ_{g} during the scanning portion of the underlying linear temperature program is then calculated by linear interpolation between the values derived in the adjoining isothermal portions of the underlying linear temperature program. The method of interpolation is illustrated by FIG. 12.

5. Calculate the instantaneous calibration constant: At each point, the actual heat flow phase φ_{g}, as calculated in the previous step, is used as an argument in a universal calibration function to obtain the specific heat calibration constant K appropriate to the actual experimental conditions extant for that particular point.

6. Calculate the real and imaginary components of the specific heat: C' and C" are calculated at each point by solving the following set of simultaneous equations:

C' cos (ψ_{g}+ψ_{T})-C" sin (ψ_{g}+ψ_{T})=Kφ_{cos}/(T_{a}ω)

C' sin (ψ_{g}+ψ_{T})+C" cos (ψ_{g}+ψ_{T})=Kφ_{sin}/(T_{a}ω)

where T_{a} =(T_{cos} ^{2} +T_{sin} ^{2})^{1/2} and ω is the circular frequency corresponding to the applied oscillation's period. The value K in the above equations for calculation of the real component of the specific heat (C') and the imaginary component of the specific heat (C") is the instantaneous calibration constant calibrated in step 5, above.

7. Smooth the calculated signals: φ_{DC}, C' and C" are smoothed at each point by normalized numerical integration over an interval consisting of exactly an integer number of oscillation periods and centered on that point. Each calculated value is associated with the centroid of the integration interval.

The following experimental data were obtained using a Perkin-Elmer DSC-7 "power compensation" Differential Scanning Calorimeter connected to a Perkin-Elmer TAC-7/DX Thermal Analysis Controller that communicates with a Perkin-Elmer Unix 7-Series data station. All samples used in the experiments are readily available commercial products. Sample sizes are as indicated below.

FIG. 4 shows the glass transition of polystyrene (PS), measured in a cooling run (β_{0} =-1 K/min, Oscillation amplitude T_{a} =1K, Period=100 sec, Sample weight=17.452 mg).

The heat capacity C_{a} is calculated from the average heat flow φ_{D}. C_{a} is equal to the value obtained with a conventional DSC and is identical to C.sub.β. The inflection point in C_{a} occurs at a lower temperature than that of C'. In contrast to C', the T_{g} measured using C_{a} depends on β_{0}. The inflection point of the real (energy storage) part C', is correlated with the peak in the imaginary (energy loss) part, C". Both the shape and the temperature dependence of C' and C" are in accord with the theories of relaxation in glass transition.

The heat capacities C_{abs} (absolute heat capacity) and C_{a} (average heat capacity), and their difference C_{a} -C_{abs}, are shown for the same measurement as in FIG. 4.

FIG. 5 depicts the prior art calculation (from the '775 patent). C_{a} -C_{abs} indeed exhibits a peak; however, it is located at lower temperature than the glass transition (as calculated from C') and is dependent on the cooling rate β_{0}. As explained with regard to eq. (28), this calculated value is non-quantitative regarding the relaxation process.

The difference between the prior art ('775 patent) and the present invention is shown for the measurement of FIG. 4. As is apparent, C" and C_{a} -C_{abs} exhibit a markedly different dependence on the temperature, with only the former having its peak correctly at the inflection point (glass transition temperature T_{g}) of the real part and absolute value of the complex specific heat.

Glass Transition of Polystyrene (PS), measured in a heating run (β_{0} =2 K/min, Oscillation amplitude T_{a} =1K, Period=50 sec, Sample Weight=17.452 mg). The sample is identical to that used for the run of FIG. 4.

C_{a} exhibits the same behavior as seen with a conventional DSC. An enthalphy relaxation peak is superimposed on the glass transition. C' has an inflection point similar to that of FIG. 4.

Calculation following the prior art ('775 patent). The interpretation of C_{a} -C_{abs} suffers from the same difficulties as in FIG. 5: only C" has its peak correctly at the inflection point (glass transition temperature T_{g}) of the real part and absolute value of the complex specific heat.

Heating curve for quench cooled PET (β_{0} =2 K/min, Oscillation amplitude T_{a} =1K, Period=60 sec, Sample Weight=5.842 mg).

Three transitions can be seen: the glass transition around 70° C., the recrystallization around 120° C. and the melting around 200° C. The glass transition exhibits the same behavior as discussed for polystyrene. The recrystallization is a transition of the strongly undercooled melt in the polymer crystal. The melt is far removed from equilibrium. The transition is possible in only one direction and is therefore only barely seen in the modulated signal. Only C" has a small peak. C' can be used as a baseline in the evaluation of C_{a}. As far as the melting is concerned, C' exhibits a change at lower temperatures, while C" remains unchanged in that range. The peak maximum of C" occurs at a somewhat larger temperature than that of C'. Using irreversible thermodynamics, these curves give information on enthalpy changes and entropy.

Calculation following the prior art ('775 patent). C_{a} -C_{abs} is really the difference between two curves obtained under dissimilar experimental conditions. It can be interpreted only intuitively, and not quantitatively.

The difference between the prior art ('775 patent) and the present invention is shown for the measurement of FIG. 9: since, as explained with regard to FIG. 9, the recrystallization cannot affect the modulated signal, it is essentially not seen in either C' or C" while strongly present in C. In contrast, C_{a} -C_{abs}, the prior art "non-rapidly reversible" component, erroneously exhibits a strong peak at the recrystallization temperature. In addition, the latter quantity also evinces apparently unexplainable behavior around the phase transition temperature.

Patent Citations

Cited Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US2975629 * | Jun 6, 1958 | Mar 21, 1961 | Patent & Licensing Corp | Test equipment for determining temperature change characteristics of materials |

US3165915 * | Jul 25, 1961 | Jan 19, 1965 | Abbott Gaynor L | Determination of thermal properties of materials |

US3263484 * | Apr 4, 1962 | Aug 2, 1966 | Perkin Elmer Corp | Differential microcalorimeter |

US3271996 * | Nov 24, 1965 | Sep 13, 1966 | Ferenc Paulik | Apparatus for thermal analysis |

US3314279 * | Jul 8, 1964 | Apr 18, 1967 | Ct Nat De La Recherche | Apparatus for recording and regulating temperature during differential thermal analysis |

US3339398 * | Mar 30, 1964 | Sep 5, 1967 | Chevron Res | High sensitivity differential thermal analysis apparatus and method |

US3360993 * | Aug 27, 1965 | Jan 2, 1968 | Air Force Usa | Single thermocouple differentiating method and system |

US3417604 * | Aug 12, 1965 | Dec 24, 1968 | Atomic Energy Authority Uk | Methods and apparatus for differential thermal analysis |

US3527081 * | Feb 23, 1966 | Sep 8, 1970 | Ici Ltd | Differential scanning calorimeter |

US3527923 * | Oct 5, 1967 | Sep 8, 1970 | Perkin Elmer Corp | Single element heater arrangement for an analytical instrument |

US3732722 * | Aug 20, 1971 | May 15, 1973 | Perkin Elmer Corp | Material holder |

US3789662 * | Oct 26, 1971 | Feb 5, 1974 | Instrumentation Labor Inc | Calorimetry |

US4040288 * | Mar 5, 1976 | Aug 9, 1977 | Kotelnikov Grigory Vladimirovi | Differential microcalorimeter |

US4095453 * | Feb 25, 1977 | Jun 20, 1978 | E. I. Du Pont De Nemours And Company | Differential thermal analysis cell |

US4255961 * | Oct 17, 1978 | Mar 17, 1981 | University Of Va. Alumni Patents Foundation | Differential calorimeter based on the heat leak principle |

US4350446 * | Nov 3, 1980 | Sep 21, 1982 | E. I. Du Pont De Nemours And Company | Method and apparatus for calorimetric differential thermal analysis |

US4517021 * | Oct 28, 1983 | May 14, 1985 | A. E. Staley Manufacturing Company | Semi-crystalline fructose |

US4568198 * | May 26, 1983 | Feb 4, 1986 | Budapesti Muszaki Egyetem | Method and apparatus for the determination of the heat transfer coefficient |

US4579462 * | May 20, 1985 | Apr 1, 1986 | Trans-Met Engineering, Inc. | Dew point measuring apparatus |

US4587279 * | Aug 31, 1984 | May 6, 1986 | University Of Dayton | Cementitious building material incorporating end-capped polyethylene glycol as a phase change material |

US4690569 * | May 22, 1986 | Sep 1, 1987 | Qualtronics Corporation | Thermal profile system |

US4747698 * | Apr 30, 1986 | May 31, 1988 | International Business Machines Corp. | Scanning thermal profiler |

US4783174 * | Aug 18, 1986 | Nov 8, 1988 | Max-Planck-Gesellschaft Zur Foerderung Der Wissenschaften E.V. | Differential isoperibol scanning calorimeter |

US4812051 * | Apr 30, 1986 | Mar 14, 1989 | Magyar Optikai Muvek | Apparatus for investigating thermal transformations |

US4838706 * | Mar 19, 1987 | Jun 13, 1989 | The Provost, Fellows And Scholars Of The College Of The Holy And Undivided Trinity Of Queen Elizabeth Near Dublin | Thermal analysis |

US4840496 * | Feb 23, 1988 | Jun 20, 1989 | The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration | Noncontact temperature pattern measuring device |

US4848921 * | Sep 22, 1986 | Jul 18, 1989 | Bodenseewerk Perkin-Elmer & Co., Gmbh | Apparatus and method for power compensation in a differential scanning calorimeter |

US4855667 * | Jun 13, 1988 | Aug 8, 1989 | E. I. Du Pont De Nemours And Company | Parallel plate dielectric analyzer |

US4899046 * | Feb 9, 1989 | Feb 6, 1990 | Schlumberger Industries, S.A. | Optical sensor of physical magnitude |

US4899102 * | Apr 12, 1989 | Feb 6, 1990 | E. I. Du Pont De Nemours And Company | Electrode system for a parallel plate dielectric analyzer |

US4902107 * | May 15, 1989 | Feb 20, 1990 | Canon Kabushiki Kaisha | Ferroelectric liquid crystal optical device having temperature compensation |

US4902558 * | Sep 29, 1988 | Feb 20, 1990 | Henriksen Henning R | Method for protecting skin from hazardous chemicals |

US4912971 * | Jan 10, 1989 | Apr 3, 1990 | Edwards Development Corp. | System for recovery of petroleum from petroleum impregnated media |

US4928254 * | Apr 28, 1988 | May 22, 1990 | Knudsen Arne K | Laser flash thermal conductivity apparatus and method |

US4956793 * | Jun 24, 1988 | Sep 11, 1990 | Honeywell Inc. | Method and apparatus for measuring the density of fluids |

US5045798 * | Jan 24, 1990 | Sep 3, 1991 | Ta Instruments, Inc. | Planar interdigitated dielectric sensor |

US5046858 * | Jun 20, 1990 | Sep 10, 1991 | Schlumberger Technologies Limited | Temperature reference junction for a multichannel temperature sensing system |

US5065106 * | Feb 25, 1991 | Nov 12, 1991 | Ta Instruments, Inc. | Apparatus and method for analyzing dielectric properties using a single surface electrode and force monitoring and adjusting |

US5080495 * | Aug 28, 1990 | Jan 14, 1992 | Mitsui Toatsu Chemicals, Inc. | Method and apparatus for measuring thermal diffusivity by ac joule-heating |

US5095278 * | Jun 29, 1989 | Mar 10, 1992 | Ta Instruments, Inc. | Planar interdigitated dielectric sensor |

US5098196 * | Jan 4, 1991 | Mar 24, 1992 | The Perkin-Elmer Corporation | Circuit for heating and sensing with a single element |

US5135833 * | Jan 18, 1991 | Aug 4, 1992 | Canon Kabushiki Kaisha | Electrostatic image developing toner and fixing method |

US5141331 * | Feb 17, 1989 | Aug 25, 1992 | Oscar Oehler | Ultrasonic temperature measurement and uses in optical spectroscopy and calorimetry |

US5152607 * | Dec 6, 1991 | Oct 6, 1992 | Solomat Partners L.P. | Process for analyzing relaxation spectra and resonances in materials |

US5165792 * | Mar 1, 1991 | Nov 24, 1992 | Ta Instruments, Inc. | Method and apparatus for high resolution analysis |

US5167857 * | Oct 18, 1990 | Dec 1, 1992 | Canon Kabushiki Kaisha | Lactic acid derivative, liquid crystal composition containing same and liquid crystal device |

US5224775 * | Mar 2, 1992 | Jul 6, 1993 | Ta Instruments, Inc. | Method and apparatus for modulated differential analysis |

US5225766 * | Dec 24, 1991 | Jul 6, 1993 | The Perkin Elmer Corporation | High impedance current source |

US5248199 * | May 26, 1992 | Sep 28, 1993 | Ta Instruments, Inc. | Method and apparatus for spatially resolved modulated differential analysis |

US5346306 * | May 7, 1993 | Sep 13, 1994 | Ta Instruments, Inc. | Method and apparatus for modulated differential analysis |

EP0051266A2 * | Oct 28, 1981 | May 12, 1982 | E.I. Du Pont De Nemours And Company | Method and apparatus for calorimetric differential thermal analysis |

EP0380414A2 * | Jan 24, 1990 | Aug 1, 1990 | Solomat Partners L.P. | Method for analysing the relaxation spectra and the resonances in materials |

EP0559362A1 * | Feb 23, 1993 | Sep 8, 1993 | Ta Instruments, Inc. | Method and apparatus for modulated differential analysis |

FR2289905A1 * | Title not available | |||

GB2222885A * | Title not available | |||

JPH02311748A * | Title not available | |||

JPH03237346A * | Title not available | |||

JPS6413446A * | Title not available | |||

SU277318A1 * | Title not available | |||

SU309258A1 * | Title not available | |||

SU325548A1 * | Title not available | |||

SU932293A1 * | Title not available | |||

SU1133525A1 * | Title not available | |||

SU1437755A1 * | Title not available | |||

SU1689828A1 * | Title not available |

Non-Patent Citations

Reference | ||
---|---|---|

1 | * | "Application Brief", TA, No. 47, Dec. 1987, 3 pages. |

2 | * | "Parameters Based on Scanning Calorimetry Data", Thermal Ananlysis, Vol. 2, Proc. of the Fourth ICTA, Budapest, Jul.8-13, 1974, pp. 513-518. |

3 | * | Azumi, T., et al., " Thermal Coductivity Measurement by AC-Calorimetry, Measurement in the Direction of Sample Zhickness", Part IV, Proceedings of the Eighth Japan Symposium on Thermophysical Properties, Jul. 22-24, 1987, pp. 171-174. |

4 | * | Bahra, M., Elliott, D., and Ryan, R., " Novel Approach to thermal Analysis of Thin Films", Journal of Thermal Analysis, Vol. 38, No. 4, Apr. 1992, pp. 543-555. |

5 | * | Ban, S., Takahashi, Y., Tanase, H., and Hasegawa, J., " Heat Curing Behaviour of Light-cured Composite resins Investigated by Dynamic Differential Scanning Calorimetry", Dental Materials Journal, Vol. 9, No. 2, Dec. 1990, pp. 153-162. |

6 | * | Barrall, E. M., II, and Johnson, J. F., " Differential Scanning Calorimetry Theory and Applications", Thermal Characterization Techniques, Mercel Dekker, Inc., New York, 1970, Chpt. 1, pp.1-39. |

7 | * | Barrio, M., Font, J., Muntasell, J., and Tamarit, J. Ll., " AC Calorimetry Applied to Powdered Samples", Journal of Thermal Analysis, Vol. 37, 1991, pp. 39-54. |

8 | * | Baturic-Rubcic, J., Leontic B., and Lukatela, J., " Exploration of a New Method of Small Sample AC-Calorimetry at Low Temperatures", Fizika,8, No. 2-3, J uly 1976, pp. 45-51. |

9 | * | Beiner, M., et al., " Onste of the Dynamic Glass Transition in Poly(nbutylmethacrylate)", Physica A, Statistical and Theoretical Physics, Vol. 201, 1993, pp. 72-78. Cassel, R. B., and Gray A. P., " An Automated Commercial Scanning Calorimeter System", Quatrieme Conference Internationale De Thermodynamique Chimique, pp. 25-33, ( Undated). |

10 | * | Bil, V. S., and Samardukov, E. V., " Rapid Estimation Method of Non-Isothermal Crystalization and the Polymers Phase State. |

11 | * | Birge, N. O., and Nagel, S. R., " Specific-Heat Spectroscopy of the Glass Transition", Physical Review Letters, Vol. 54, No. 25, June 24, 1985, pp. 2674-2677. |

12 | * | Birge, N. O., Nagel, S. R., " Wide-Frequency Specific Heat Spectrometer", Review of Scientific Instruments, Vol. 58, No. 8, Aug. 1987, pp. 1464-1470. |

13 | * | Birge, Norman O., " Specific-Heat Spectroscopy of Glycerol and Propylene Glycol near the Glass Transition", Physical Review B, Vol. 34, No. 3, Aug. 1, 1986. |

14 | * | Black, S. G., and Dixom, G. S., " Annealing Study of Irreversibility in the Chain-Melting Transition in Lipids", Biophysical Journal, Vol. 33, No. 2, Part 2, Feb. 1981, p. 163a. |

15 | * | Black, S. G., and Dixon, G. S., " AC Calorimetry of Dimyristoylphosphatidylcholine Multilayers: Hysteresis and Annealing near the Gel to Liquid-Crystal Transition", Biochemistry, Vol. 20, No. 23, 1981, pp. 6740-6741. |

16 | * | Black, S. G., and Dixon, G. S., " AC Calorimetry Study of Annealing Phenomena Near the Chain-Melting Transition in Dimyristoyl Phosphatidylcholine Bilayers", Bulletin of the American Physical Society, Vol. 26, No. 3, March 1981, P. 305. |

17 | * | Black, S., and Dixon, G. S., " AC Calorimetry of Lipid Suspensions", Bulletin of the American Physical Society, Series II, Vol. 24, No. 3, March 1979, p. 321. |

18 | * | Black, S., and Dixon, G. S., " Differential AC Calorimetry of Lipid Dispersions", Federation Proceedings, Vol. 39, No. 6, May 1, 1980. |

19 | * | Black, Steven Gayle, " A. C. Calorimetry of DMPC Liposomes", Ph. D. Dissertation, Oklahoma State Univ., 1982. |

20 | * | Brennan, W. P., " Some Applications of Differential Scanning Calorimetry for the Analysis of Polymers"; Thermochimica Acta, Vol. 17, No. 3, Dec. 1976, pp. 285-293. |

21 | * | Brennan, W. P., Miller, B., and Whitwell, J. C., " Rate of Change of Reference Temperature in DSC and DTA", Thermochimica Acta, Vol. 2, No. 4, June 1971, pp. 354-356. |

22 | * | Campbell, D., and White, J.R., " Chapter 12 - Thermal Analysis", Polymer Characterization. Physical Techniques, Champman and Hall, 1989, pp. 301-326. |

23 | * | Cassel, B., " New Techniques in DSC: Differential Heat Capacity Determinations for Maximum Accuracy", The Pittsburgh Conference on Anal. Chemistry, Clevland, Ohio, Mar. 1974. |

24 | * | Cassel, B., and Gray, A. P., " Thermal Analysis Simplifies Accelerated Life Testing of Plastics", Plastics Engineering, May 1977, pp. 56-58. |

25 | * | Charsley, E. L., Duke, P. W., Manning, N. J., Marshall, S. J., and Reading, M., " Applications of a New Low Temperature Differential Scanning Calorimeter", Journal Of Thermal Analysis, Vol. 33, No. 1, 1988, pp. 379-384. |

26 | * | Chiu, J., " Dynamic Thermal Analysis of Polymers. An Overview", Polymer Characterization by Thermal Methods of Analysis, Marcel Dekker, Inc., New York, 1974, pp. 3-23. |

27 | * | Daniels, T. C., Thermal Ananlysis, A Halsted Press Book, 1973, pp. 122-135. |

28 | * | Dixit, R. N., Pattalwar, S. M., Shete, and Basu, B. K., " Modified Heat-Puls e Techniques for High resolution Specific Heat Measurements", Rev. Sci. Instrum., Vol. 60, No. 1, July 1989, pp. 1351-1352. |

29 | * | Dixon, G. S., and Black, S. G., Butler, C. T., and Jain, A. K., " A&V Differential AC Calorimeter for Biophysical Studies", Analytical Biochemistry, Vol. 121, No. 1, March 15, 1982, pp. 55-61. |

30 | * | Dollimore, D., Gamlen, G. A., Rouquerol, J., Rouquerol, F., and Reading, M., "Comparison of Cyclic CRTA, CRTA, TG and Isothermal Methods for Finding the Activation Energy for the Decomposition of Calcium Carbonate", Proceedins of the Sceond European Symposium on Thermal Analysis, Sept. 1-4, 1981, pp. 99-102. |

31 | * | Donth, E., " The Size of Cooperatively Rearranging Regions at the Glass Transition", Journal of Non-Crystalline Solids, Vol. 53, No. 3, Dec. 3, 1982, pp. 325-330. |

32 | Drong, K., Lamprecht, I., and Plesser, Th., "Calorimetric Measurements of an Intermittency Phenomenon in Oscillating Glycolysis in Cell-Free Extracts from Yeast, " Thermochimica Acta, vol. 151, 1989, pp. 69-81. | |

33 | * | Drong, K., Lamprecht, I., and Plesser, Th., Calorimetric Measurements of an Intermittency Phenomenon in Oscillating Glycolysis in Cell Free Extracts from Yeast, Thermochimica Acta, vol. 151, 1989, pp. 69 81. |

34 | * | Elder, John P., " Purity Analysis by Dynamic and Isothermal Step Differential Scanning Calorimetry", Purity Determination: By Thermal Methods, Apr. 25, 1983, pp. 50-60. |

35 | * | Festa, C., and Ceccanti, N., " A Differential Calorimeter for Measuring Heats of Solution with a Pulse Time Modulation System", Annali di Chimica, Vol. 70, No. 9-10, 1980, pp. 431-37. |

36 | Filimonov, V. V., Potekhin, Matveev, S. V., and Privalov, P. L., "Thermodynamic Analysis of Scanning Microcalorimetric Data," Biophysical Chemistry, vol. 87, 1987, pp. 435-444. | |

37 | * | Filimonov, V. V., Potekhin, Matveev, S. V., and Privalov, P. L., Thermodynamic Analysis of Scanning Microcalorimetric Data, Biophysical Chemistry, vol. 87, 1987, pp. 435 444. |

38 | * | Flynn, J. H., " Instrumental Limitations upon the Measurement of Temperature and Rate of Energy Production By Differential Scanning Calorimetry", Thermal Analysis, Vol. 1, Proceedings of the Third ICTA, Davos, Aug. 23-28, 1971, pp. 127-138. |

39 | * | Freire, E., and Biltonen, R. L., " Statistical Mechanical Deconvolution of Thermal Transitions in Macromolecules. I. Theory and Applications to Homogeneous Systems", Biopolymers, Vol. 17, No. 2, Feb. 1978, pp. 463-479. |

40 | * | Freire, E., van Osdol, W. W., Mayorga, O. l., and Sanchez-Ruiz, J. M., " Calorimetrically Determined Dynamics of Complex Unfolding Transitions in Proteins", Annu. Rev. Biophys., Biophys. Chem. 1990, Vol. 19, pp. 159-188. |

41 | * | Garland, C. W., " Calorimetric Studies of Liquid Crystal Phase Transitions: AC Techniques", Phase Transitions in Liquid Crystals, Plenum Press, New York, Chpt. 11, 1992, pp. 175-187. |

42 | * | Garland, Carl W., " High Resolution AC Calorimtery and Critical Behaviour at Phase Transitions", Thermochimica Acta, 88, 1985, pp. 127-142. |

43 | * | Graebner, J. E., " Modulated-Bath Calorimetry", Rev. Sci. Instrum., Vol. 60, No. 6, June 1989, pp. 1123-1128. |

44 | * | Gray, A. P. and Casey, K., " Thermal Analysis and the Influence of Thermal History on Polymer Fusion Curves", Polymer Letters, Vol. 2, 1964. |

45 | * | Gray, A. P., " Crystallinity of Polymers By Scanning Calorimetry", Society of Plastics Engineers 29th ANTEC, May 0-13, 1971, p. 288. |

46 | * | Gray, A. P., " Polymer Crystallinity Determinations By DSCII", Thermochimica Acta, Vol. 1, No. 6, Dec. 1970, pp. 563-579. |

47 | * | Gray, A. P., " The Calorimetry of the NBS-ICTA Temperature Standards", Thermal Analysis, Vol. 3, Proc. Fourth ICTA, Budapest, 1974, pp. 991-1003. |

48 | * | Gray, A. P., and Brenner, N., " Rapid Heat Capacity Measurement on Polymers", American Chemical Society Division of Polymer Chemistry, Vol. 6, No. 2, Sept. 1965, pp. 956-957. |

49 | * | Griffin, V. J., and Laye, P. G., " Differential Thermal Ananlysis and Differential Scanning Calorimetry", Thermal Analysis Techniques and Applications, The Royal Society of Chemistry, 1992, pp. 17-30. |

50 | * | Guerrero, A., Reading, M., Grillet, Y., Rouquerol,J., Boitiaux, J. P., and Cosyns, J., " Influence of Dispersion on the Energies of Absorption: H2, Co, Propylene and propyne on Supported Pd or Pt", Atoms, Molecules and Clusters, Vol. 12, No. 1-4, 1989, pp. 583-586. |

51 | * | Haga, H., Onodera, A., and Shiozaki, Y., " Specific Heat and Critical Indices Associated with Normal-Incommensurate Phase Transition in Dipotassium Tetroachlorozincate and Diammonium Tetraflouroberyllate", Ferroelectrics, Vol. 125, 1992, pp. 123-128. |

52 | * | Hatta, I., and Ikushima, A. J., " Studies on Phase Transitions by AC Calorimetry", Japanese Journal of Applied Physics, Vol. 20, No. 11, Nov. 1981, pp. 1995-2011. |

53 | * | Hatta, Ichiro, " Recent Development of AC Calorimetry", Netsu Sokutei no Shinpo, Vol. 3, pp. 1-11,(Publication date is believed to be prior to 1987). |

54 | * | Hay, J. N., " Applications of Thermal Analysis of Polymers", Thermal Analysis - Techniques and Applications, The Royal Society of Chemistry, 1992, pp. 156-161, 267-270. |

55 | * | Imaizumi, S., and Garland, C. W., " Heat Capacity Associated with Phase Transitions in Micellar Cesium Perfluoro-Octanoate Solutions", Journal of the Physical Society of Japan, Vol. 58, No. 2, Feb. 1989, pp. 597-601. |

56 | * | Imaizumi, S., Suzuki, K., Hatta, I., " AC Calorimeter for Liquid Including Suspension of Biological Materials", Rev. SCI, Instrum., Vol. 54, No. 9, Sept. 1983, pp. 1180-1185. |

57 | * | Jain, A. K., and Dixon, G. S., " AC Calorimetry of Phospholipid Dispersions", Joint Meeting of Biophysical Society (22nd Annual Meeting) and America Physical Society (March Meeting), March 27-30, 1978, p. 214a. |

58 | * | Jung, D. H., Kwon, T. W., Bae, D. J., Moon, I. K., and Jeong, Y. H., " Fully Automated Dynamic Calorimeter", Meas. Sci. Technol. 1992, pp. 475-484. |

59 | * | Kambe, H. et al., "Kinetic Investigation of Polymerization Reaction with Differential Scanning Calomiter", Thermal Analysis, Vol. 2, Proceedings of the Second ICTA, Worcester, Aug. 18-23, 1968, pp. 1071-1083. |

60 | * | Kasting, G. B., Lushington, K. J., and Garland, C. W., " Critical Heat Capacity Near the Nematic-Smectic-A Transition in Octyloxycyanobiphenyl in the Range 1-2000 bar", Physical 1 Review B, Vol. 22, No.1, July 1, 1980, pp. 321-331. |

61 | Kraftmakher, Y. A., "Modulation Calorimetry," Compendium of Thermophysical Property Measurement Methods, Plenum Press, New York, vol. 1, Chapter IV, 1984, pp. 591-641. | |

62 | * | Kraftmakher, Y. A., Modulation Calorimetry, Compendium of Thermophysical Property Measurement Methods, Plenum Press, New York, vol. 1, Chapter IV, 1984, pp. 591 641. |

63 | * | Kubicar, L., " An Equipment for Measuring Thermophysical Quantities by Means of Heat-Pulse Methods in the Temperature Region Between 20-300 degrees centigrade, Fiz. Cas (Czechoslovakia) Vol. 22, No. 3, 1972, pp. 129-136. |

64 | * | Kubicar, L., " Trends in the Methods of Measurement of Therophysical Properties in the Solid State", Thermochimica Acta, Vol. 110, Feb. 1, 1987, pp. 209-215. |

65 | * | Kubo, R., " The Fluctuation-Dissipation Theorem", Reports on Progress in Physics, Vol. XXIX, Part I, 1966, pp. 255-284. |

66 | * | Langmaack, H. J., " Optimierung von Kohlenwasserstoffgelen aus Analytisch Definierbaren Komponenten, 2. Mitteilung: Kohlenwasserstoffgele als Grundlagen fur W/0-Cremes", Fette Seifen Anstrichmitte, No. 4, April 1985, pp. 163-166. |

67 | * | Maesono, A., et al., " Thermal Analysis and Their Instruments", HYBRIDS, Vol. 6, No. 4, 1990, pp. 26-37. |

68 | * | Maesono, Akikazu, and Kato, Ryozo, " Recently Developed Instruments Relevant to AC Calorimetry", Netsu Sokutei no Shinpo, Vol. 5, 1987, pp. 71-78. |

69 | * | Mayorga, A. L., van Osdol, W. W., Lacomba, J. L., and Freire, E., " Frequency Spectrum of Enthalpy Fluctuations Associated with Macromolecular Transitions", Proc. Natl. Acad Sci. USA, Vol. Dec. 1988, pp. 9514-9518. |

70 | * | Mayorga, O. L., and Freire, E., " Dynamic Analysis of Differential Scanning Calorimetry Data", Biophysical Chemistry, Vol. 27, 1987, pp. 87-96. |

71 | * | Melveger, A. J., and Vetrecin, R. B., " IDSC Heat of Fusion Measurements of Polymers: Improving Accuracy and Precision", Thermal Methods in Polymer Analysis, The Franklin Institute Press, Philadelphia, 1977, pp. 63-75. |

72 | Mitchell, J., "DSC: A New Design for Evaluating the Thermal Behavior of Materials," International Laboratory, Feb. 28, 1991, pp. 44-48. | |

73 | * | Mitchell, J., DSC: A New Design for Evaluating the Thermal Behavior of Materials, International Laboratory, Feb. 28, 1991, pp. 44 48. |

74 | * | Nakamura, N., and Teramoto, Y., " Visco-elastic Measurement Using the Thermochemical Ananlyser with Enhanced Function", Netsu Sokutei no Shinpo, Vol. 5, 1987, pp. 79-86. |

75 | * | Narayanaswamy, O. S., " A Model of Structural Relaxation in Glass", Journal of the American Ceramic Society, Vol. 54, No. 10, Oct. 1971, pp. 491-498. |

76 | * | Nottenburg, R., Freeman, M., Riaeshwar, K., and DuBow, J., " Concurrent Dielectric Analysis-Differential Thermal Analysis, Analytical Chemistry, Vol. 51, No. 8, Jul. 1979, pp. 1149-1155. |

77 | * | O Neill, M. J., and Gray, A. P., " Design Considerations in Advanced Systems for Differential Scanning Calorimetry", Thermal Analysis, Vol. 1, Proc. Third ICTA, Davos, 1971, pp. 279-294. |

78 | * | Palenzona, A., " Dynamic Differential Calorimetry of Intermetallic Compounds", Thermochimica Acta, 5, 1973, pp. 473-480. |

79 | * | Point, R., Petit, L., and Gavelle, P. C., " Reconstruction of Thermokinetics from Calorimetric Data by Means of Numerical Inverse Filters", Journal of Thermal Analysis, Vol. 17, No. 2, Dec. 1979, pp. 383-393. |

80 | * | Reading, M., " A Comparative Study of Thermoanalytical Methods and Their Application to Selected Transition Metal Oxysalts", Ph. D. Dissertation, Univ. of Salford, 1983. |

81 | * | Reading, M., " Modulated Differential Scanning Calorimetry - A Way Forward in Metals Characterization", TRIP, Vol. 1, 8, Aug. 1993, pp. 248-253. |

82 | * | Reading, M., " The Kinetics of Heterogenous Solid State Decomposition Reactions", Thermochimica Acta, Vol. 135, 1988, 37-57. |

83 | * | Reading, M., and Rouquerol, J., " Controlled Rate Thermal Analysis Using an Infra-Red Gas Analyser", Thermochimica 1985, pp. 299-302. |

84 | * | Reading, M., Dollimore, D., and Whitehead, R., " The Measurement of Meaningful Kinetic Parameters for Solid State Decomposition Reactions", Journal of Thermal Ananlysis, Vol. 37, No. 9, Sept. 1991, pp. 2165-2188. |

85 | * | Reading, M., Dollimore, D., Rouquerol, J., and Rouquerol, F., " The Measurement of Meaningful Activation Energies", Journal of Thermal Analysis, Vol. 29, No. 4, Jul./Aug. 1984, pp. 775-785. |

86 | * | Reading, M., et al., " A New Approach to the Calorimetric Invetsigation of Physical and Chemical Transactions", Journal of Theraml Analysis, Vol. 40, No. 3, 1993, pp. 949-955. |

87 | * | Salamati-Mashhad, H., Dixon, G. S., and Martin, J. J., " Heat Capacity of Mn¹-x ZnxF² for x<0.1", Journal of Applied Physics, Vol. 53, No. 3, Par-t-2, March1982, pp. 1929-1930. |

88 | * | Sauerbrunn, S. R., Crowe, B. S., and Reading, M., " Modulated Differential Scanning Calorimetry", American Laboratory, Aug. 1992, pp. 44, 46-47. |

89 | * | Schiedeshoff, G. M., " Computer-controlled, Small Sample AC Calorimetry at Low Temperatures and in High Magnetic Fields", Rev. Sci. Instrum., Vol. 58, No. 9, Sept. 1987, pp. 1743-1745. |

90 | * | Staub, H., and Perron, W., " New Method of Purity Determinatiol Means of Calorimetric Differential Thermal Analysis", Analytical Chemistry, Vol. 46, No. 1, Jan. 1974, pp. 128-130. |

91 | * | Sullivan, Paul F., and Seidel G., " Steady-State, ac-Temperature Calorimetry", Physical Review, Vol.173, No. 3, Sept. 1968, pp. 679-685. |

92 | * | Tanasijczuk, O. S., and Oja, T., " High Resolution Calorimeter for the Investigation of Melting in Organic and Biological Materials", Rev. Sci. Instrum., 49(11), Nov. 1978, pp. 1545-1548. |

93 | * | Utshick, H., Gobrecht, B., Fleischhauer, C., Treffurth, A., and Muller, H., " On the Complex Influence of the Experimental Parameters and the Properties of the Substances on the Representation of Solid-Liquid Transitions Studied with a Differential Scanning Calorimeter", Journal Of Thermal Analysis, Vol. 33, 1988, pp. 297-304. |

94 | van Osdol, W. W., Mayorga, O. L., and Freire, E., "Multi-frequency Calorimetry of the Folding/Unfolding Transition of Cytochrome C," Biophysical Journal, vol. 59, 1991, pp. 48-54. | |

95 | * | van Osdol, W. W., Mayorga, O. L., and Freire, E., Multi frequency Calorimetry of the Folding/Unfolding Transition of Cytochrome C, Biophysical Journal, vol. 59, 1991, pp. 48 54. |

96 | * | Vargas, R. A., and Angulo, H., " Phase Transition and Proton Disordering in some Ferroelectric Hydrogen-bonded Lead Salts", Solid States Ionics. Diffusion and Reactions, Vol. 53-56, Part II, July/Aug. 1992, pp. 1302-1304. |

97 | * | Vargas, R. A., and Torijano, E., " Phase Behaviour Of RBH2PO4, and CSH2PO4, in the fast-ion Regime", Solid State Ionics. Diffusion and Reactions, Vol. 59, No. 3,4, Feb. 1993, pp. 321-324. |

98 | * | Watson, E. S., O Neil, M. J., Justin, J. and Brenner, N.," A Differential Scanning Calorimeter for Quantitative Differential Thermal Analysis", Benchmark Papers in Analytica: Chemistry, Thermal Analysis, Vol.2, Dowden, Hutchinson & Ross, 1976, pp. 172-177. |

99 | * | Wendtland, W., " Differential Thermal Ananlysis and Differential Scanning Calorimetry", Thermal Analysis, Chpt. 5, 3rd Edit., John Wiley and Sons, Inc., Vol. 19, 1986, pp. 1, 213-299. |

100 | * | Westwood, A. R., " Analysis of the Curing Reactions of Thermosetting Polymers by DSC", Thermal Analysis, Vol. 3, Proceedings of the Third ICTA, Davos, Aug. 23-28, 1971, pp. 169-177. |

101 | * | Willard, P. E., " Evaluation of Initiators and Fillers in Diallyl Phthalate Resins by Differential Scanning Calorimetry", FMC Corp., Marcel Dekker, Inc., New York, 1974, pp. 33-41. |

102 | * | Willis, J. M., et al., " The Effect of Carrier Gas on Rates of Crystallization of Isotactic Polypropylene Obtained by Differential Scanning Calorimetry", Thermal Analysis, Vol. 2, Proc. of the Seventh ICTA, Ontario, 1982, pp. 1030-1039. |

103 | * | Yao, H., and Hatta, I., " An AC Microcalorimetric Method for Precise Heat Capacity Measurement in a Small Amount of Liquid", Japanese Journal of Applied Physics, Vol. 27, No. 1, an. 1988, pp. l121-l122. |

104 | Yimin Jin, Andreas Boller and Bernhard Wunderlich, "Heat Capacity Measurement by Modulated DSC at Constant Temperature", contained in Proceedings of the Twenty-Second Conference of the North American Thermal Analysis Society, Kathryn R. Williams, Ed., pp. 59-64, publication date unknown, date of proceedings: Sep. 19-22, 1993. | |

105 | * | Yimin Jin, Andreas Boller and Bernhard Wunderlich, Heat Capacity Measurement by Modulated DSC at Constant Temperature , contained in Proceedings of the Twenty Second Conference of the North American Thermal Analysis Society, Kathryn R. Williams, Ed., pp. 59 64, publication date unknown, date of proceedings: Sep. 19 22, 1993. |

Referenced by

Citing Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US5788373 * | May 17, 1996 | Aug 4, 1998 | Mettler-Toledo Gmbh | Method and apparatus for performing single differential thermal analysis |

US6071008 * | Jan 28, 1998 | Jun 6, 2000 | Nagoya University | Method of measuring heat capacity of sample |

US6079873 * | Jun 30, 1998 | Jun 27, 2000 | The United States Of America As Represented By The Secretary Of Commerce | Micron-scale differential scanning calorimeter on a chip |

US6095679 * | Apr 21, 1997 | Aug 1, 2000 | Ta Instruments | Method and apparatus for performing localized thermal analysis and sub-surface imaging by scanning thermal microscopy |

US6146012 * | Jan 15, 1999 | Nov 14, 2000 | Seiko Instruments Inc. | Differential thermal analyzer |

US6146013 * | Jun 25, 1998 | Nov 14, 2000 | Mettler-Toledo Gmbh | Differential thermal analysis system including dynamic mechanical analysis |

US6220748 * | Jan 15, 1999 | Apr 24, 2001 | Alcoa Inc. | Method and apparatus for testing material utilizing differential temperature measurements |

US6491425 * | Jun 1, 2000 | Dec 10, 2002 | Ta Instruments, Inc. | Method and apparatus for performing localized thermal analysis and sub-surface imaging by scanning thermal microscopy |

US6551835 * | Sep 26, 2000 | Apr 22, 2003 | Mettler-Toledo Gmbh | Method and apparatus for thermally analyzing a material |

US6632015 * | Apr 18, 2001 | Oct 14, 2003 | Seiko Instruments Inc. | Thermal analysis apparatus |

US6641300 * | Jan 29, 2002 | Nov 4, 2003 | Waters Investment, Ltd. | Differential scanning calorimeter |

US20010038660 * | Apr 18, 2001 | Nov 8, 2001 | Jun Nagasawa | Thermal analysis apparatus |

US20100195695 * | Jan 27, 2010 | Aug 5, 2010 | Mettler-Toledo Ag | Thermo-analytical instrument |

EP2214005A1 * | Feb 3, 2009 | Aug 4, 2010 | Mettler-Toledo AG | Thermo-Analytical Instrument |

WO2002021103A1 * | Sep 6, 2001 | Mar 14, 2002 | Aissor S.A.R.L. | Apparatus for stabilising the state of gaseous media in particular for (micro) (nano) manipulations or micro-measurements |

WO2002066956A1 * | Feb 15, 2001 | Aug 29, 2002 | Alcoa Inc. | Method and apparatus for testing material utilizing differential temperature measurements |

Classifications

U.S. Classification | 374/10, 702/136, 374/E17.001, 374/31 |

International Classification | G01N25/20, G01K17/00, G01N25/48 |

Cooperative Classification | G01K17/00, G01N25/4866, G01N25/4833 |

European Classification | G01N25/48A4B, G01N25/48B2, G01K17/00 |

Legal Events

Date | Code | Event | Description |
---|---|---|---|

Sep 23, 1994 | AS | Assignment | Owner name: PERKIN-ELMER CORPORATION, THE, CONNECTICUT Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:SCHAWE, JUERGEN;MARGULIES, MARCEL;REEL/FRAME:007149/0591;SIGNING DATES FROM 19940621 TO 19940706 |

Dec 24, 1996 | CC | Certificate of correction | |

Feb 25, 2000 | FPAY | Fee payment | Year of fee payment: 4 |

Jul 27, 2000 | AS | Assignment | Owner name: PERKINELMER INSTRUMENTS LLC, CONNECTICUT Free format text: CHANGE OF NAME;ASSIGNOR:ELMER PERKIN LLC;REEL/FRAME:011007/0254 Effective date: 20000201 Owner name: PERKIN ELMER LLC, CONNECTICUT Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:PERKIN-ELMER CORPORATION;REEL/FRAME:011007/0258 Effective date: 20000718 |

Feb 18, 2004 | FPAY | Fee payment | Year of fee payment: 8 |

Feb 27, 2008 | FPAY | Fee payment | Year of fee payment: 12 |

Mar 3, 2008 | REMI | Maintenance fee reminder mailed |

Rotate